Is it farther or further?
late 14c., the Greek river of the Underworld, cognate with Greek stygos "hatred," stygnos "gloomy." Oaths sworn by it were supremely binding and even the gods feared to break them. The adjective is Stygian.
In classical mythology, one of the rivers of Hades, across which Charon ferried the souls of the dead. The gods occasionally swore by the river Styx. When they did so, their oath was unbreakable.